The Bad Plus is all about worlds colliding. A classic rock drumbeat meets a hard-bop piano line, a dirty bass blues confronts a tinkling swing, time signatures change faster than a Victorian lady’s mind, and even the band’s look is at odds with itself. Pianist Ethan Iverson sports sharp suits and ties while bassist Reid Anderson and drummer Dave King perform in jeans and Converse sneakers. But in the face of all these dichotomies, one thing remains true of the group: At every moment, they are playing together, and it’s the most natural thing in the world.

No words were exchanged as The Bad Plus settled on stage for its second set at Yoshi’s on April 14, night two of three in Oakland. King reached out a tattooed arm to adjust a microphone over his cymbal, Iverson gave an elegant shoulder roll as he took the bench and Anderson just smiled. They started with a song called “Mint,” followed by “Anthem For Earnest,” whose title is appropriate because at certain moments the tune is undeniably a rock anthem. Rubato piano falls in line with the raucous bass and drum beat just long enough to evoke power chords and head-banging, when suddenly all three parts drop in volume to play a unison theme that feels oddly like “Hernando’s Hideaway.” The effect can only be described as epic.

The Bad Plus’ repertoire is mostly originals, and after songs like “My Friend Metatron” and “Seven Minute Mind,” a few silver bullets in the group’s arsenal began to cut the air. The band has taken the concept of a hit and let it blossom into an explosion. Members’ personal connections boarder on ESP, conjuring images of the three of them living together in some sort of jazz tree house, Swiss Family Robinson-style, when the truth is they don’t even write their songs together.

“We all play piano,” said Anderson after the show. “Songs come to the group fully formed, and we arrange them afterwards.” That explains why drumbeats can feel like melodies and piano lines often become percussive. Every instrument is malleable in the group’s hands during composition. King even whipped out a squeaky ET doll and used it as a percussion instrument on Iverson’s new song “Everything’s In.”

“My daughter got it as a birthday present,” King said. “I took one look at it and said, ‘That’s mine.’”

Every tune originates from its own unique concept, a fact that Anderson enacted as he introduced “Beryl Loves To Dance.”

“It’s about this girl named Beryl,” he said, gesturing around the bass. “And she’s kind of shy and a little awkward. She’s around junior high age, which is an awkward age for all of us, and some of us never get over it and that’s fine. But like many outwardly shy people, she has a really rich inner life, and so this song is called ‘Beryl Loves To Dance.’ But the thing is, she only dances when she’s alone. And even though she’s not a very good dancer, it doesn’t matter because in her head she’s fantastic.”

As they played through the tune, a spirited refrain twirled through each of the parts with such energy it lifted Iverson up off the bench. The bass held down a hook that seemed to make anything possible, and syncopated breaks peppered each section. It was during the applause that my date, new to The Bad Plus, kissed me on the cheek and mouthed the words “thank you.”